1. Analytic Hierarchy Process Multiple-criteria decision-making Real world decision problems –multiple, diverse criteria –qualitative as well as quantitative information Comparing apples and oranges? Spend on defence or agriculture? Open the refrigerator - apple or orange?

2. AHP Information is decomposed into a hierarchy of alternatives and criteria Information is then synthesized to determine relative ranking of alternatives Both qualitative and quantitative information can be compared using informed judgements to derive weights and priorities

3. Example: Car Selection Objective –Selecting a car Criteria –Style, Reliability, Fuel-economyCost? Alternatives –Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata

4. Hierarchical tree - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata - Civic - Saturn - Escort - Miata

5. Ranking of criteria Weights? AHP –pair-wise relative importance [1:Equal, 3:Moderate, 5:Strong, 7:Very strong, 9:Extreme] StyleReliabilityFuel Economy Style Reliability Fuel Economy 1/11/23/1 2/11/14/1 1/31/41/1

6. Ranking of priorities Eigenvector [Ax = x] Iterate 1. Take successive squared powers of matrix 2. Normalize the row sums Until difference between successive row sums is less than a pre-specified value

7. 1 0.5 3 2 14 0.333 0.251.0 3.0 1.75 8.0 5.3332 3.0 14.0 1.1666 0.6667 3.0 squared Row sums 12.75 22.3332 4.8333 39.9165 Normalized Row sums 0.3194 0.5595 0.1211 1.0 New iteration gives normalized row sum 0.3196 0.5584 0.1220 Difference is: - 0.3194 0.5595 0.1211 0.3196 0.5584 0.1220 = - 0.0002 0.0011 - 0.0009

8. Preference Style.3196 Reliability.5584 Fuel Economy.1220

9. Ranking alternatives Style Civic Saturn Escort 1/1 1/44/1 1/6 4/1 1/14/1 1/4 1/4 1/4 1/11/5 Miata6/1 4/1 5/1 1/1 CivicSaturnEscortMiata Reliability Civic Saturn Escort 1/1 2/15/1 1/1 1/2 1/1 3/1 2/1 1/5 1/3 1/11/4 Miata1/1 1/2 4/1 1/1 CivicSaturnEscortMiata.1160.2470.0600.5770 Eigenvector.3790.2900.0740.2570

10. Fuel Economy (quantitative information) Civic Saturn Escort Miata 34 27 24 28 113 Miles/gallon Normalized.3010.2390.2120.2480 1.0

11. - Civic.1160 - Saturn.2470 - Escort.0600 - Miata.5770 - Civic.3790 - Saturn.2900 - Escort.0740 - Miata.2570 - Civic.3010 - Saturn.2390 - Escort.2120 - Miata.2480

12. Ranking of alternatives Style Reliability Fuel Economy Civic Escort Miata Saturn.1160.3790.3010.2470.2900.2390.0600.0740.2120.5770.2570.2480 *.3196.5584.1220 =.3060.2720.0940.3280

13. Handling Costs Dangers of including Cost as another criterion –political, emotional responses? Separate Benefits and Costs hierarchical trees Costs vs. Benefits evaluation –Alternative with best benefits/costs ratio

14. Cost vs. Benefits MIATA$18K.333.9840 CIVIC$12K.2221.3771 SATURN$15K.2778.9791 ESCORT$9K.1667.5639 Cost Normalized Cost Cost/Benefits Ratio

15. Complex decisions Many levels of criteria and sub-criteria

16. Application areas –strategic planning –resource allocation –source selection, program selection –business policy –etc., etc., etc.. AHP software (ExpertChoice) –computations –sensitivity analysis –graphs, tables Group AHP